Techniques for single particle 3D reconstruction from electron micrographs are currently capable of achieving sub-nanometer resolutions for homogeneous biological samples. Cells are highly dynamic and during a functional cycle organelles and macromolecular complexes undergo multiple morphological and conformational changes. Understanding the relationship between conformation and function requires the study of more complex macromolecular assemblies. When purified in an almost physiological state, these preparations exhibit high levels of heterogeneity and pose new challenges for accurate physical measurements. 3D electron microscopy and image processing must be ready to take on these highly challenging specimens. However, techniques for analyzing heterogeneous samples to high resolution are missing. The completion of this research project will provide new techniques needed for efficiently analyzing multiple structures of flexible macromolecular complexes to high resolution. We will develop new algorithms for analyzing the variability associated with heterogeneous complexes. We will devise tools for the systematic partitioning of data in a low-dimensional vector space obtained by applying different multivariate statistical methods to projection data. The partitioning of image data will be combined with automated 3D reconstruction algorithms, thus intimately linking the analysis of image variations to 3D structure variations. New techniques will be developed for alignment, classification and partitioning of sets of 3D volumes with missing data of arbitrary geometry and directionally variable signal-to-noise ratios. Simultaneous translational and rotational 2D and 3D alignment algorithms will be extended to increase accuracy. The transfer function correction will not only be applied to the projections, but, in addition, it will be integrated into the 3D Radon inversion algorithm to obtain the highest resolution possible in every step of the data analysis. The proposed developments will provide a new set of tools for determining to high resolution the 3D structures of heterogeneous macromolecular assemblies present in different conformational and aggregational states. All new programs developed in this project will be made available under an open source license to the general research community. During their functional cycle subcellular components undergo multiple conformational and morphological changes. This research project develops methods to study this conformational variability. Understanding the relation between function and shape of macromolecular complexes will contribute to the understanding the molecular basis of many diseases.